Complexity-constrained spatially coupled LDPC codes based on protographs

Spatially coupled low-density parity-check (SC-LDPC) codes are often thought as codes with very long block lengths. However, they can be decoded through sliding window (SW) decoders achieving near-optimal performance when the window size is a few times larger than the code syndrome former constraint length. This makes SC-LDPC codes with short constraint length suitable for low-latency transmissions, and they can even outperform their block code counterparts. Complexity of SW decoders increases linearly with the window size and with the number of decoding iterations. When complexity is constrained, an optimal trade-off between the window size and the maximum number of decoding iterations has to be found. In this paper, we propose a PEXIT-based method to find the best trade-off for codes with short syndrome former constraint length. We consider codes based on protographs, and validate the results of the PEXIT-based method through Monte Carlo simulations.

[1]  D. Costello,et al.  Approaching capacity with asymptotically regular LDPC codes , 2009, 2009 Information Theory and Applications Workshop.

[2]  Dariush Divsalar,et al.  Accumulate repeat accumulate codes , 2004, ISIT.

[3]  J. Thorpe.  Low-Density Parity-Check (LDPC) Codes Constructed from Protographs , 2003 .

[4]  Paul H. Siegel,et al.  Windowed Decoding of Protograph-Based LDPC Convolutional Codes Over Erasure Channels , 2010, IEEE Transactions on Information Theory.

[5]  Stephan ten Brink,et al.  Convergence behavior of iteratively decoded parallel concatenated codes , 2001, IEEE Trans. Commun..

[6]  Dariush Divsalar,et al.  Capacity-approaching protograph codes , 2009, IEEE Journal on Selected Areas in Communications.

[7]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[8]  Marco Chiani,et al.  Protograph LDPC Codes Design Based on EXIT Analysis , 2007, IEEE GLOBECOM 2007 - IEEE Global Telecommunications Conference.

[9]  Gerhard Fettweis,et al.  Efficient message passing scheduling for terminated LDPC convolutional codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[10]  Rüdiger L. Urbanke,et al.  Spatially coupled ensembles universally achieve capacity under belief propagation , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[11]  Mark F. Flanagan,et al.  Design of LDPC code ensembles with fast convergence properties , 2014, 2015 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom).

[12]  Vahid Jamali,et al.  An efficient complexity-optimizing LDPC code design for the binary erasure channel , 2014, 2014 8th International Symposium on Turbo Codes and Iterative Information Processing (ISTC).

[13]  D. Millar,et al.  Iteration-Aware LDPC Code Design for Low-Power Optical Communications , 2016, Journal of Lightwave Technology.

[14]  Kamil Sh. Zigangirov,et al.  Time-varying periodic convolutional codes with low-density parity-check matrix , 1999, IEEE Trans. Inf. Theory.

[15]  Marco Baldi,et al.  Design and Analysis of Time-Invariant SC-LDPC codes with Small Constraint Length. , 2017 .

[16]  Rüdiger L. Urbanke,et al.  The capacity of low-density parity-check codes under message-passing decoding , 2001, IEEE Trans. Inf. Theory.